Emulators run software written for other systems. RetroArch is a frontend for many cores, from NES and SNES to PlayStation. PPSSPP emulates the PSP, Delta covers Nintendo handhelds and consoles and succeeds GBA4iOS, and Provenance is a multi-system frontend that also targets Apple TV. SameBoy is an accurate Game Boy and Game Boy Color emulator.
Computer emulators are here too: Mini vMac for early 68K Macs, DOSPad for DOSBox, ActiveGS for the Apple II and IIGS, MAME4iOS for arcade machines, and iSH, which emulates x86 to run Linux. Several of these, including RetroArch, PPSSPP and Delta, now have App Store links after Apple allowed emulators in 2024. Most emulators are GPL licensed. They ship without games or BIOS files, so you need your own legally obtained copies.